We consider that the direct production of a single neutralino in proton-proton collision at the CERN Large Hadron Collider focusing on the lightest neutralino is possibly a candidate for the dark matter and escapes detection. We present a comprehensive investigation of the dependence of total cross sections of the processes $pp(q\bar q)\rightarrow\widetilde��_{i}^{0}\widetilde{\text{g}}$, $pp(q \text{g}) \rightarrow\widetilde��_{i}^{0}\widetilde{q}_{L,R}$, $pp(q\bar{q}^{\prime})\rightarrow\widetilde��_{i}^{0}\widetilde��_{j}^{+}$ at tree-level and $pp(\text{g}\text{g})\rightarrow\widetilde��_{i}^{0}\widetilde{\text{g}}$ at one-loop level, on the center-of-mass energy, on the $M_2$-$��$ mass plane, on the squark mass and on the $\tan��$ for the Constrained Minimal Supersymmetric Standard Model and the three extremely different scenarios in the Minimal Supersymmetric Standard Model. In particular, the cross section of the process $p p \to \widetilde��_{2}^{0}\widetilde��_{1}^{+}$ in the gaugino-like scenario can reach about 0.6 (1.7) pb at a center-of-mass energy of $\sqrt{s}=$ 7 (14) TeV. We derive therefrom that our results might lead to new aspects corresponding to experimental explorations, and these dependencies might be used as bases of experimental research of the single neutralino production at hadron colliders.

33 pages, 29 figures, 3 tables